Differentical equations, dynamical systems and optimal control

On group properties of epidemics equation

A. V. Mastikhin

Bauman Moscow State Technical University, ul. Baumanskaya 2-ya, 5/1, 105005, Moscow, Russia

Abstract: We consider a time-homogeneous Markov process on discret set of states known as Weiss (simple) epidemic process. For exponential (double) generating function of the transition probabilities we consider system of first and second Kolmogorov equations. The system exact solution was obtained by using Lie group methods. We also discuss the opportunity of using the same method in the case of general epidemic process.

Keywords: Markov process, exponential (double) generating function, first and second Kolmogorov equation, Fourier method, simple epidemic, general epidemic, infinitesimal symmetry generator, Lie algebra.

UDC: 517.9

MSC: 60J27

Received April 18, 2017, published December 12, 2017

DOI: 10.17377/semi.2017.14.120

Bibliographic databases:

•